(1+1×2/1)+(2+2×3/1)+(3+3×4/1)+……+(20+20×21)初一数学

来源：百度知道编辑：UC知道时间：2024/05/30 02:42:23

要用关于n的代数式来表示s

拆，首先1+2+3+……+n+……提出来，为n(n+1)/2;1*2+2*3+3*4+……中a(n)=n(n+1)=n^2+n,又拆成n^2和n在求和，n^2的为n(n+1)(2n+1)/6,n的同上，所以结果为n(n+1)(2n+1)/6 + n(n+1)

式子是这样吧：
[1+1/(1×2)]+[2+1/(2×3)]+[3+1/(3×4)+……+[20+1/(20×21)]
=(1+2+3+...+20)+(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/20-1/21)
=210+(1-1/21)=210+20/21

s=n*(n+1)/2+n/(n+1)

(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) 1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1+1/1+2+1/1+2+3.........+1/1+2+3.....100 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=? (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000) (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8) (1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2) 1+1/2+1+1/3+1+1/4+......+1/100=?